The field of the invention is systems and methods for magnetic resonance imaging (“MRI”). More particularly, the invention relates to systems and methods for parallel MRI image reconstruction.
Depending on the technique used, many MRI scans currently require many minutes to acquire the necessary data used to produce medical images. The reduction of this scan time is an important consideration, since reduced scan time increases patient throughput, improves patient comfort, and improves image quality by allowing for a reduction in subject motion artifacts. Many different strategies have been developed to shorten the scan time of MRI scans.
One such strategy is referred to generally as “parallel MRI” (“pMRI”). In general, pMRI techniques achieve a reduction in scan time by undersampling the data acquisition. For example, every other phase encoding step can be skipped in order to reduce scan time by a factor of two. In these instances, however, aliasing artifacts are introduced into images that are reconstructed with conventional image reconstruction techniques. To overcome these aliasing artifacts, pMRI techniques generally use spatial information from an array of radio frequency (“RF”) receiver coils to substitute for the spatial encoding that would otherwise be provided by RF pulses and magnetic field gradients foregone in the pMRI technique.
Each of the spatially independent receiver coils of the coil array carries certain spatial information that can be identified by its unique spatial sensitivity profile. This information is utilized to achieve a complete spatial encoding of the received MR signals, for example, by combining the simultaneously acquired data received from each of the separate coils. As noted above, pMRI techniques allow an undersampling of k-space, typically by reducing the number of acquired phase-encoded k-space sampling lines, while keeping the maximal extent covered in k-space fixed. The combination of the separate MR signals produced by the separate receiver coils enables a reduction of the acquisition time required for an image as compared to the time required for a conventional k-space data acquisition. This “acceleration” is related to the number of the receiver coils in the coil array. Thus, the use of multiple receiver coils acts to accelerate imaging speed, without increasing gradient switching rates or RF power.
Two categories of exemplary pMRI techniques include those methods that generate a single image from a multi-coil data set, and those methods that generate an image for each coil in the coil array. Single image reconstruction methods include the method known in the art as sensitivity encoding (“SENSE”), which seeks to estimate the underlying image common to all coil receivers. Such techniques, while statistically efficient, require explicit knowledge of the spatial sensitivity functions for each coil sensor. Typically, sensitivity functions are estimated using a separate “calibration” scan that lengthens the exam, is challenging to perform in dynamic applications, and unavoidably propagates error into the reconstructed images.
Coil-by-coil methods include those known in the art as simultaneous acquisition of spatial harmonics (“SMASH”) and generalized autocalibrating partially parallel acquisitions (“GRAPPA”). With GRAPPA, k-space lines near the center of k-space are sampled at the Nyquist frequency, while k-space lines in the peripheral regions of k-space are acquired with a degree of undersampling. The center k-space lines are referred to as so-called autocalibration signal (“ACS”) lines, which are used to determine weighting factors that are utilized to synthesize, or reconstruct, the missing k-space lines. In particular, a linear combination of individual coil data is used to create the missing lines of k-space. The coefficients for the combination are determined by fitting the acquired data to the more highly sampled data near the center of k-space.
In lieu of explicit sensitivity information, methods such as GRAPPA learn inter-coil correlations from the ACS lines and use this information to jointly reconstruct all coil images. In practice, coil-by-coil methods are often more robust and versatile than single image reconstruction strategies; however, most coil-by-coil methods require the explicit formation of an inter-coil correlation function that can lead to error propagation, and may limit their applicability to acquisitions with special structured sampling patterns.
Parallel imaging is a widely used strategy for accelerating MRI acquisitions. Auto-calibrated coil-by-coil methods, such as GRAPPA, have become increasingly popular because they do not require a separate calibration scan, like SENSE does, nor do they require an explicit estimation of coil sensitivity profiles. These features make auto-calibrated pMRI techniques attractive for time-limited and dynamic applications like cardiac imaging. However, auto-calibrated pMRI techniques still typically require the explicit formation of a mathematical operator that describes intercoil correlations. Because this operator must itself be estimated from the measured data, its use during reconstruction unavoidably propagates error into the final generated images. Moreover, auto-calibration techniques inherently comprise a joint estimation of both the target images and the system model (e.g., the GRAPPA kernel). This joint-estimation corresponds to a challenging bilinear optimization problem, in which effort is spent to explicitly estimate the system model that is ultimately discarded post-reconstruction.
In an attempt to circumvent these foregoing problems with auto-calibration techniques, M. Lustig et al., proposed a method for coil-by-coil reconstruction of phased-array MRI data using a global Fourier-domain low-rank matrix completion technique, as described in “Calibration Parallel Imaging by Structured Low-Rank Matrix Completion,” Proc. of the ISMRM, 2010; 2870. This reconstruction technique exploits the tendency of a Hankel matrix formed by stacking rasterizations of small k-space blocks to be low-rank. This technique, however, has limited scalability. For example, the memory footprint of the constructed Hankel matrix can be well over an order of magnitude larger than that of the target image set, and performing singular value decompositions on such large matrices is computationally challenging. Also, the generalization of this k-space approach to incorporating physical signal models, such as the Dixon model for fat-water separation techniques, is not straightforward.